Method and Apparatus for Public-Key Cryptography Based on Error Correcting Codes

4. The method of claim 1 , further comprising: transmitting said ciphertext vector x through said communication medium.

5. The method of any of claim 1 , further comprising: receiving the ciphertext vector x from the communication medium; and decrypting the ciphertext vector x to obtain the cleartext vector u by using a private key comprising the private linear block code.

6. The method of claim 1 , wherein a=a 1 +a 2 , with a 1 and a 2 being two z×n matrices, and wherein R = [ a 1 a 2 ] T · [ b d ] , where d is a z×n matrix.

7. The method of claim 6 , wherein d=1−b, where 1 is an all-one z×n matrix.

8. The method of any of claim 1 , wherein the public key further comprises a second part, the second part representing z error constraints, z being a positive integer with z<n, and wherein the error vector fulfils said z error constraints.

9. The method of claim 8 , wherein the error constraints are equivalent to a condition e·R=0.

10. The method of claim 1 , wherein the matrix a represents the z error constraints, being equivalent to the condition a·e T =0.

11. The method of claim 1 , wherein the matrix a represents the z error constraints, being equivalent to the condition a·e T =γ, with γε GF(p).

12. The method of claim 9 , wherein the second part of the public key is the matrix a.

13. The method of claim 1 , wherein the private linear block code is a quasi-cyclic (QC) linear block code, n k and r are multiples of a positive integer q (n=n 0 ×q, k=k 0 ×q, r=r 0 ×q) and matrices S, R, T and, where applicable, G or H are formed by circulant sub-matrices with size q×q, a circulant matrix being a square matrix in which each row is obtained through a rightwards cyclic shift of the previous row by one position.

14. The method of claim 1 , wherein the matrix T is a sum of m generalized permutation matrices Π i , i=1, . . . , m, m being a positive integer, each generalized permutation matrix Π i having only one non-zero element in each row and column, whose value is selected among the p−1 non-zero elements of GF(p).